Curve cryptography

A Hardware Architecture for Elliptic Curve Cryptography and Lossless Data Compression. We present a hardware architecture that combines Elliptic Curve Cryptography (ECC) and lossless data compression in a single chip.

The paper gives an introduction to elliptic curve cryptography (ECC) and how it is used in the implementation of digital signature (ECDSA) and key agreement (ECDH) Algorithms. The paper discusses the implementation of ECC on two finite fields, prime field and binary field.

This paper presents an approach related to authenticate mutually a RFID (Radio Frequency Identification) tag from a RFID reader by using the cryptography based on Elliptic curve. Our proposal mutual authentication lies on the Elliptic curve discrete logarithm problem, which is considered the core in order to fight against all of attacks like replay attack, forgery attack and man-in-the-middle attack. Scientifically, we prove not only the accuracy and the security of our approach, but also its performance in the mutual authentication between a RFID tag and a reader. ...

During the last three decades, public academic research in cryptography has exploded.
While classical cryptography has been long used by ordinary people, computer
cryptography was the exclusive domain of the world’s militaries since the World War
II. Today, state-of the-art computer cryptography is practiced outside the secured
walls of the military agencies. The laypersons can now employ security practices that
can protect against the most powerful adversaries.

The paper discusses the implementation of ECC on two finite fields, prime field and binary field. It also gives an overview of ECC implementation on different coordinate systems called the projective coordinate systems.

We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables eﬃcient arithmetic. The scaling technique may be used to improve multiplication and inversion in ﬁnite ﬁelds. We present an eﬃcient inversion algorithm that utilizes the structure of scaled modulus.

The Elliptic Curve Cryptography (ECC) is evolving as an important cryptography, and shows a promise to be an alternative of RSA. Small size, high security and other features characterize ECC. Based on the theory of ECC, this paper analyzes its advantages over other cryptographies and focuses on its principle.

For an equivalent level of security, elliptic curve cryptography uses shorter key sizes and is
considered to be an excellent candidate for constrained environments like wireless/mobile
communications. In FIPS 186-2, NIST recommends several ﬁnite ﬁelds to be used in the
elliptic curve digital signature algorithm (ECDSA). Of the ten recommended ﬁnite ﬁelds,
ﬁve are binary extension ﬁelds with degrees ranging from 163 to 571. The fundamental
building block of the ECDSA, like any ECC based protocol, is elliptic curve scalar mul-
tiplication.

In this paper, we present the results of our implementation of elliptic curve cryptography (ECC) over the ﬁeld GF (p) on an 80-MHz, 32-bit ARM microprocessor. We have produced a practical software library which supports variable length implementation of the elliptic curve digital signature algorithm (ECDSA).

(BQ) The Handbook of information and communication security covers some of the latest advances in fundamentals, cryptography, intrusion detection, access control, networking (including extensive sections on optics and wireless systems), software, forensics, and legal issues. The editors intention, with respect to the presentation and sequencing of the chapters, was to create a reasonably natural flow between the various sub-topics. The book is divided into 2 parts, part 1 from chapter 1 to chapter 20.

Implementation of the cryptographic algorisms based on elliptic curves (ECs) over VFFs provides signiﬁcantly higher performance than the implementation of the EC-based algorithms, in which the ECs are deﬁned over the ground ﬁelds and extension ﬁnite ﬁelds of polynomials.

Objectives of Chapter 1: To define three security goals; to define security attacks that threaten security goals; to define security services and how they are related to the three security goals; to define security mechanisms to provide security services; to introduce two techniques, cryptography and steganography, to implement security mechanisms

Recently, identity based cryptography based on pairing operations deﬁned over elliptic curve points has stimulated a signiﬁcant level of interest in the arithmetic of ternary extension ﬁelds, GF (3n ).